# Tagged Questions

This tag is suited for questions involving Turing machines. Not to be confused with finite state machines and finite automata.

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### How can Busy beaver($10 \uparrow \uparrow 10$) have no provable upper bound?

This wikipedia article claims that the number of steps for a $10 \uparrow \uparrow 10$ state (halting) Turing Machine to halt has no provable upper bound: "... in the context of ordinary ...
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### Turing Machine recognizability

I'm trying to go over some review problems regarding Turing Machine recognizability, and am still pretty confused about the following problems. This is the only information we are given in the problem ...
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### Are there any Turing-undecidable problems whose undecidability is independent of the Halting problem?

To be more specific, does there exist a decision problem $P$ such that given an oracle machine solving $P$, the Halting problem remains undecidable, and given an oracle machine solving the Halting ...
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### Why do we believe the Church-Turing Thesis?

The Church-Turing Thesis, which says that the Turing Machine model is at least as powerful as any computer that can be built in practice, seems to be pretty unquestioningly accepted in my exposure to ...
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### Milton Green's lower bounds of the busy beaver function

Wikipedia states that Milton Green demonstrated in 1964, that the busy beaver function $\Sigma(n)$ has the lower bound $$\Sigma(2k)>3\uparrow^{k-2}3$$ I read the talk about the busy beaver ...
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### Turing Machine Variation

Hi i'm trying to figure out this question: Give a formal definition of multihead-multitape Turing machine. Then show how such a machine can be simulated by a standard Turing machine Can someone ...
### Let $L_{UIUC}$ = $\{ \langle M \rangle$ : $L(M)$ contains the string $UIUC\}$. Prove that $L_{UIUC}$ is undecidable.
Been stumped as to why the following proof works. Note: I have taken this proof directly from here. Proof by reduction from $A_{TM}$. Suppose that $L_{UIUC}$ were decidable and let $R$ be a Turing ...
I'm given the set $T = \{\langle M, w\rangle : M$ is a Turing Machine that accepts $w$ reversed whenever it accepts $w \}$ and I want to show it's undecidable but recognizable. (I'm using the bracket ...